MSC2020 · 14Gxx

Arithmetic problems in algebraic geometry; Diophantine geometry

Arithmetic problems in algebraic geometry; Diophantine geometry [See also 11Dxx, 11Gxx]

3 mapped entries · Browse and filter all →

Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

14G05Rational points1 14G10Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)0 14G12Hasse principle, weak and strong approximation, Brauer-Manin obstruction0 14G15Finite ground fields in algebraic geometry1 14G17Positive characteristic ground fields in algebraic geometry0 14G20Local ground fields in algebraic geometry0 14G22Rigid analytic geometry0 14G25Global ground fields in algebraic geometry0 14G27Other nonalgebraically closed ground fields in algebraic geometry0 14G32Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)0 14G35Modular and Shimura varieties0 14G40Arithmetic varieties and schemes; Arakelov theory; heights0 14G45Perfectoid spaces and mixed characteristic0 14G50Applications to coding theory and cryptography of arithmetic geometry1 14G99Arithmetic problems in algebraic geometry; Diophantine geometry0

Mapped problems

OP-12043Number theoryOpen

Ihara constant over $\mathbb{F}_2$ ( $C_{33}$ )

Ihara constant over mathbb F 2 : determine C 33 or improve its bounds; the repository records 0.316999... (lower) and sqrt 2 -1 approx 0.41421 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-11959Number theorySolved

Many Rational Points on a Genus-2 Curve

Many Rational Points on a Genus-2 Curve. Moderately interesting problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

OP-11954CryptographyOpen

The Elliptic-Curve Discrete Logarithm Problem (ECDLP)

The Elliptic-Curve Discrete Logarithm Problem (ECDLP). Major advance problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026